BEGIN:VCALENDAR
VERSION:2.0
PRODID:talks.ox.ac.uk
BEGIN:VEVENT
SUMMARY:Sharpness for the speed of the random walk on the simple exclusion
process - Guillaume Conchon-Kerjan (King College London)
DTSTART;VALUE=DATE-TIME:20240520T140000
DTEND;VALUE=DATE-TIME:20240520T150000
UID:https://talks.ox.ac.uk/talks/id/3c3a26b5-d678-4ef6-9756-f9b92b7a2959/
DESCRIPTION:The random walk on dynamic environments\, such as the simple e
xclusion process (SEP) on a d-dimensional lattice\, has attracted consider
able attention in the last decade. In this model\, a random walker moves a
t each unit of time to a neighbouring vertex\, with a drift that depends o
n whether its current location is occupied or not by a SEP particle.\nWe w
ill focus on the case d=1\, when occupied sites have a drift to the right\
, and empty sites a drift to the left. The parameter of interest will be t
he density of particles: when it is large (resp. small)\, the random walk
has a positive (resp. negative) speed.\nSince the SEP is conservative and
mixes slowly\, a natural question is whether there are strong trapping eff
ects\, as in the more classical setting of static environments. Could it b
e for instance that for a non-empty interval of intermediate densities\, t
he random walk has zero speed? We give a negative answer\, showing that th
e speed is strictly increasing with the density.\nThe proof uses a compari
son with a finite-range model (via renormalisation)\, and an original coup
ling to circumvent the bad mixing properties of the SEP.\nThis is joint wo
rk with Daniel Kious and Pierre-François Rodriguez.\nSpeakers:\nGuillaume
Conchon-Kerjan (King College London)
LOCATION:Venue to be announced
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/3c3a26b5-d678-4ef6-9756-f9b92b7a2959/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Sharpness for the speed of the random walk on the simple
exclusion process - Guillaume Conchon-Kerjan (King College London)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Title TBC
DTSTART;VALUE=DATE-TIME:20240513T140000
DTEND;VALUE=DATE-TIME:20240513T150000
UID:https://talks.ox.ac.uk/talks/id/64013476-f512-4cfa-910d-6b3dd3c2b38c/
DESCRIPTION:\nSpeakers:\nMatthew Buckland (University of Oxford)
LOCATION:Venue to be announced
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/64013476-f512-4cfa-910d-6b3dd3c2b38c/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Title TBC
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:CLTs for Poisson Functionals via the Malliavin-Stein Method - Tara
Trauthwein (University of Oxford)
DTSTART;VALUE=DATE-TIME:20240429T140000
DTEND;VALUE=DATE-TIME:20240429T150000
UID:https://talks.ox.ac.uk/talks/id/26b105a9-014e-4ac3-88ea-e982bad28671/
DESCRIPTION:Poisson Functionals encompass a vide variety of quantities\, r
anging from edge-functions derived from random geometric graphs to solutio
ns of SDEs with Lévy noise. In this talk\, we will examine the use of the
Malliavin-Stein method\, which allows us to derive central limit theorems
by studying what happens if we add a point (or two)\, to our graph\, say.
The main result presented here is a Malliavin-Stein-type bound which work
s under minimal moment assumptions.\nSpeakers:\nTara Trauthwein (Universit
y of Oxford)
LOCATION:Venue to be announced
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/26b105a9-014e-4ac3-88ea-e982bad28671/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:CLTs for Poisson Functionals via the Malliavin-Stein Meth
od - Tara Trauthwein (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the behavior of posterior probabilities with additional data: m
onotonicity and nonmonotonicity\, asymptotic rates\, log-concavity\, and T
urán’s inequality - Yosi Rinott (The Hebrew University of jerusalem)
DTSTART;VALUE=DATE-TIME:20240529T110000
DTEND;VALUE=DATE-TIME:20240529T120000
UID:https://talks.ox.ac.uk/talks/id/2cabb975-8148-4d9d-bd64-bb0e0d6ef9ea/
DESCRIPTION:Bayesian statisticians quantify their belief that the true par
ameter is ϑ0 by its posterior probability. The starting question of this
paper is whether the posterior at ϑ0 increases when the data are generate
d under ϑ0\, and how it behaves when the data come from ϑ ≠ ϑ0. Can i
t decrease and then increase\, and thus additional data may mislead Bayesi
an statisticians?\n\nFor data arriving sequentially\, we consider monotoni
city properties of the posterior probabilities as a function of the sample
size with respect to certain stochastic orders\, specifically starting wi
th likelihood ratio dominance.\nWhen the data is generated by ϑ ≠ ϑ0 \
, Doob's consistency theorem says that the posterior at ϑ0 converges a.s.
to zero and therefore its expectation converges to zero. We obtain precis
e asymptotic rates of the latter convergence for observations from an expo
nential family and show that the expectation of the ϑ0 -posterior under
ϑ ≠ ϑ0 is eventually strictly decreasing. Finally\, we show that in a
number of interesting cases this expectation is a log-concave function of
the sample size\, and thus unimodal. In the Bernoulli case we obtain this
result by developing an inequality that is related to Turán’s inequalit
y for Legendre polynomials.\nSpeakers:\nYosi Rinott (The Hebrew University
of jerusalem)
LOCATION:Venue to be announced
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/2cabb975-8148-4d9d-bd64-bb0e0d6ef9ea/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:On the behavior of posterior probabilities with additiona
l data: monotonicity and nonmonotonicity\, asymptotic rates\, log-concavit
y\, and Turán’s inequality - Yosi Rinott (The Hebrew University of jeru
salem)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jointly invariant measures for the KPZ equation with periodic nois
e - Evan Sorensen
DTSTART;VALUE=DATE-TIME:20240527T140000
DTEND;VALUE=DATE-TIME:20240527T150000
UID:https://talks.ox.ac.uk/talks/id/8c8e51eb-d192-4772-800c-d1af0c408ffb/
DESCRIPTION:We present an explicit coupling of Brownian bridges plus affin
e shifts that are jointly invariant for the Kardar-Parisi-Zhang equation w
ith periodic noise. These are described by Pitman-like transforms of indep
endent Brownian bridges. We obtain these invariant measures by working wit
h a semi-discrete model known as the O'Connell-Yor polymer in a periodic e
nvironment. In that setting\, the relevant Markov process is described by
a system of coupled SDEs. We show how to transform this Markov process to
an auxiliary Markov process with a more tractable invariant measure. We d
iscuss connections of this method to works of Ferrari and Martin in the mi
d 2000s in the context of multi-species particle systems. Furthermore\, we
present an application of this work to give an explicit formula for the c
ovariance function of a limiting Gaussian process obtained from the couple
d stochastic heat equation. Based on forthcoming joint work with Ivan Cor
win and Yu Gu.\nSpeakers:\nEvan Sorensen
LOCATION:Venue to be announced
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/8c8e51eb-d192-4772-800c-d1af0c408ffb/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Jointly invariant measures for the KPZ equation with peri
odic noise - Evan Sorensen
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:A BRANCHING PARTICLE SYSTEM AS A MODEL OF PUSHED FRONTS - Julie To
urniaire (IST Austria)
DTSTART;VALUE=DATE-TIME:20231113T140000Z
DTEND;VALUE=DATE-TIME:20231113T150000Z
UID:https://talks.ox.ac.uk/talks/id/ebd7109e-57c6-4dbe-a04b-2d975d851ae0/
DESCRIPTION:We consider a system of particles performing a one-dimensional
dyadic branching Brownian motion with space-dependent branching rate $r(x
)$\, negative drift $-\\mu$\, and killed upon reaching $0$. More precisel
y\, the particles branch at rate $\\rho/2$ in $[0\,1]$\, for some $\\rho\\
geq 1$\, and at rate $1/2$ in $(1+\\infty)$. The drift $\\mu=\\mu(\\rho)$
is chosen in such a way that the system is critical.\nThis system can be s
een as an analytically tractable model for fluctuating fronts\, describing
the internal mechanisms driving the invasion of a habitat by a cooperatin
g population. \nRecent studies by Birzu\, Hallatschek and Korolev on the n
oisy FKPP equation with Allee effect suggest the existence of three classe
s of fluctuating fronts: pulled\, semi-pushed and fully-pushed fronts. \nI
n this talk\, we will focus on the pushed regime. We will show that the BB
M exhibits the same phase transitions as the noisy FKPP equation. We will
then use this particle system to explain how the internal mechanisms driv
ing the invasion shape the genealogy of an expanding population.\n\nThis t
alk is based on joint work with Félix Foutel-Rodier and Emmanuel Schertze
r.\nSpeakers:\nJulie Tourniaire (IST Austria)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/ebd7109e-57c6-4dbe-a04b-2d975d851ae0/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:A BRANCHING PARTICLE SYSTEM AS A MODEL OF PUSHED FRONTS -
Julie Tourniaire (IST Austria)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weyl law in Liouville quantum gravity - Nathanaël Berestycki (Uni
versity of Vienna)
DTSTART;VALUE=DATE-TIME:20231016T140000
DTEND;VALUE=DATE-TIME:20231016T150000
UID:https://talks.ox.ac.uk/talks/id/410aefa7-d131-4882-8d7a-b809b5649082/
DESCRIPTION:Can you hear the shape of Liouville quantum gravity (LQG)?\n\n
We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the
n-th eigenvalue grows linearly with n\, with the proportionality\nconstan
t given by the Liouville measure of the domain and a certain deterministic
constant which is computed explicitly and is\,\nsurprisingly\, strictly g
reater than its Riemannian counterpart. After explaining this result and i
ts context\, as well as some related\nestimates pertaining to the small-ti
me behaviour of the heat kernel\, I hope to also present a number of conje
ctures on the spectral geometry\nof LQG.\nThese relate both to the behavio
ur of eigenfunctions (suggesting intriguing connections with so-called "qu
antum chaos") and to that of\neigenvalues\, for which we conjecture a conn
ection to random matrix statistics.\n\nThis is joint work with Mo-Dick Won
g (Durham).\nSpeakers:\nNathanaël Berestycki (University of Vienna)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/410aefa7-d131-4882-8d7a-b809b5649082/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Weyl law in Liouville quantum gravity - Nathanaël Berest
ycki (University of Vienna)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Scaling limit of the minimal spanning trees on the PWIT. - Ome
r Angel (UBC)
DTSTART;VALUE=DATE-TIME:20231009T140000
DTEND;VALUE=DATE-TIME:20231009T150000
UID:https://talks.ox.ac.uk/talks/id/16fc4b61-8a4f-4035-a414-67b685be27b6/
DESCRIPTION:We give a new construction of the scaling limit of the minimal
spanning tree on the Poisson weighted infinite tree. The construction com
bines aspects of the stick breaking construction of Aldous' CRT from segme
nts with the construction of Brownian motion from Ito's excursion measure.
This is joint with Delphin Senizergues.\nSpeakers:\nOmer Angel (UBC)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/16fc4b61-8a4f-4035-a414-67b685be27b6/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The Scaling limit of the minimal spanning trees on the PW
IT. - Omer Angel (UBC)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:A new front in branching Brownian motion - Yujin Kim (Courant Ins
titute\, NYU)
DTSTART;VALUE=DATE-TIME:20230607T110000
DTEND;VALUE=DATE-TIME:20230607T120000
UID:https://talks.ox.ac.uk/talks/id/0c551a42-8c84-436f-9116-1ecb84e44f62/
DESCRIPTION:Branching Brownian motion (BBM) has gained lots of attention i
n recent years in part due to its significance to the universality class o
f log-correlated fields and their extremal landscapes. Recently\, J. Beres
tycki\, K.\, Lubetzky\, Mallein and Zeitouni obtained a description of the
limiting point process of the extreme values and locations of BBM in dime
nsions 2 and higher\; however\, certain details of the extremal landscape
of multidimensional BBM were washed out in that limit. In this talk\, we d
escribe a more precise limiting point process that recovers those details
and gives rise to a new object in the study of BBM\, what we call the extr
emal front. We then obtain a scaling limit for the extremal front. Joint w
ork with Ofer Zeitouni.\nSpeakers:\nYujin Kim (Courant Institute\, NYU)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/0c551a42-8c84-436f-9116-1ecb84e44f62/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:A new front in branching Brownian motion - Yujin Kim (Co
urant Institute\, NYU)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:From the Pain in the Torus to a Repulsion-Diffusion Equation - Pet
er Koepernik (University of Oxford)
DTSTART;VALUE=DATE-TIME:20230503T110000
DTEND;VALUE=DATE-TIME:20230503T120000
UID:https://talks.ox.ac.uk/talks/id/d9ffc016-58d0-4765-a39a-8f1c962287d5/
DESCRIPTION:The phenomenon that underlies what Felsenstein famously dubbed
"the pain in the torus" in 1975 can loosely be described as follows: In o
ne and two dimensions\, spatial population models with independent critica
l branching\, and diffusive spatial motion\, concentrate in increasingly f
ew well-separated clumps\, until they eventually die out. We illustrate th
is phenomenon with simulations\, and sketch a proof in the setting of supe
rBrownian motion.\nReal populations do not behave in this way\, and one of
the reasons is that individuals migrate away from overcrowded areas. This
effect can be incorporated into superBrownian motion as a pairwise repuls
ion between individuals. We explain how this relates to a certain (determi
nistic) repulsion-diffusion equation\, for which we show well-posedness an
d give conditions on the strength of the repulsion that ensure global boun
dedness of solutions.\nSpeakers:\nPeter Koepernik (University of Oxford)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d9ffc016-58d0-4765-a39a-8f1c962287d5/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:From the Pain in the Torus to a Repulsion-Diffusion Equat
ion - Peter Koepernik (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-commutative probability and fermionic stochastic quantisation
- Ajay Chandra (Imperial)
DTSTART;VALUE=DATE-TIME:20230227T140000Z
DTEND;VALUE=DATE-TIME:20230227T150000Z
UID:https://talks.ox.ac.uk/talks/id/9b2e96a8-58b2-4f63-b2b5-d915d606fb22/
DESCRIPTION:I will discuss work in progress with Martin Hairer and Martin
Peev on a singular stochastic PDE arising from a regularised (but still\n
ill-posed) Yukawa model in two dimensions. A key ingredient is an appro
ach to unbounded random variables in non-commutative probability\nwhich dr
aws on ideas from non-commutative geometry. \nSpeakers:\nAjay Chandra (Imp
erial)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/9b2e96a8-58b2-4f63-b2b5-d915d606fb22/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Non-commutative probability and fermionic stochastic quan
tisation - Ajay Chandra (Imperial)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:The expected degree distribution in transient duplication divergen
ce models - Tiffany Lo (Uppsala University)
DTSTART;VALUE=DATE-TIME:20230206T140000Z
DTEND;VALUE=DATE-TIME:20230206T150000Z
UID:https://talks.ox.ac.uk/talks/id/d5a520e6-e57d-4b59-bb56-878705ee9e55/
DESCRIPTION:We study the degree distribution of a randomly chosen vertex i
n a duplication–divergence graph\, paying particular attention to what h
appens when a non-trivial proportion of the vertices have large degrees\,
establishing a central limit theorem for the logarithm of the degree distr
ibution. Our approach\, as in Jordan (2018) and Hermann and Pfaffelhuber (
2021)\, relies heavily on the analysis of related birth–catastrophe proc
esses. This is joint work with A. D. Barbour. \nSpeakers:\nTiffany Lo (Upp
sala University)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d5a520e6-e57d-4b59-bb56-878705ee9e55/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The expected degree distribution in transient duplication
divergence models - Tiffany Lo (Uppsala University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pattern Occurrence Counts in Random Planar Maps - Michael Drmota (
TU Wien)
DTSTART;VALUE=DATE-TIME:20230123T140000Z
DTEND;VALUE=DATE-TIME:20230123T150000Z
UID:https://talks.ox.ac.uk/talks/id/7b1dd95f-4f16-4cbf-93d6-aad7952bbbef/
DESCRIPTION:Random planar maps have been studied from various aspects duri
ng the last 15 or 20 years\, including various limiting distributions for
several parameters of interest (such as the largest 2-connected component)
and local Benjamini-Schramm limits as well as scaling limits. A pattern i
s a given planar map and we say that it appears in another map if it could
be "cut out" just leaving a face. The simplest pattern is just a k-gon. I
t directly follows from the Benjamini-Schramm limit that the expected numb
er of occurrences of a given pattern is asymptotically linear in the numbe
r of edges of the random map. However\, it is a challenging problem to pro
vide a more precise limit law. The purpose of this talk is to give a surve
y on the results and methods that have used so far in order to settle this
question. It is conjectured that there is always a central limit theorem
- and all results so far support this conjecture.\nSpeakers:\nMichael Drmo
ta (TU Wien)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/7b1dd95f-4f16-4cbf-93d6-aad7952bbbef/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Pattern Occurrence Counts in Random Planar Maps - Michael
Drmota (TU Wien)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sub-diffusive scaling regimes for one-dimensional Mott variable-ra
nge hopping - David Croydon (RIMS\, Kyoto University)
DTSTART;VALUE=DATE-TIME:20230130T140000Z
DTEND;VALUE=DATE-TIME:20230130T150000Z
UID:https://talks.ox.ac.uk/talks/id/52a4341e-115a-48ee-88cf-4e32cc5f4a66/
DESCRIPTION:I will describe anomalous\, sub-diffusive scaling limits for a
one-dimensional version of the Mott random walk. The first setting consid
ered nonetheless results in polynomial space-time scaling. In this case\,
the limiting process can be viewed heuristically as a one-dimensional diff
usion with an absolutely continuous speed measure and a discontinuous scal
e function\, as given by a two-sided stable subordinator. Corresponding to
intervals of low conductance in the discrete model\, the discontinuities
in the scale function act as barriers off which the limiting process refle
cts for some time before crossing. I will outline how the proof relies on
a recently developed theory that relates the convergence of processes to t
hat of associated resistance metric measure spaces. The second setting con
sidered concerns a regime that exhibits even more severe blocking (and sub
-polynomial scaling). For this\, I will describe how\, for any fixed time\
, the appropriately-rescaled Mott random walk is situated between two\nenv
ironment-measurable barriers\, the locations of which are shown to have an
extremal scaling limit. Moreover\, I will give an asymptotic\ndescription
of the distribution of the Mott random walk between the barriers that con
tain it. This is joint work with Ryoki Fukushima (University of Tsukuba) a
nd Stefan Junk (Tohoku University).\nSpeakers:\nDavid Croydon (RIMS\, Kyot
o University)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/52a4341e-115a-48ee-88cf-4e32cc5f4a66/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Sub-diffusive scaling regimes for one-dimensional Mott va
riable-range hopping - David Croydon (RIMS\, Kyoto University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limit of an adaptive contact process - Daniel Valesin (Uni
versity of Warwick)
DTSTART;VALUE=DATE-TIME:20221128T120000Z
DTEND;VALUE=DATE-TIME:20221128T130000Z
UID:https://talks.ox.ac.uk/talks/id/7453685b-814a-429b-884d-3ce4f01ad20e/
DESCRIPTION:We introduce and study an interacting particle system evolving
on the d-dimensional torus \\Z^d_N. Each vertex of the torus can be eithe
r empty or occupied by an individual of a given type\; the space of all ty
pes is the positive real line. An individual of type \\lambda dies with ra
te one and gives birth at each neighbouring empty position with rate \\lam
bda. Moreover\, when the birth takes place\, the new individual is likely
to have the same type as the parent\, but has a small chance to be a mutan
t\; the mutation rate and law of the type of the mutant both depend on \\l
ambda. We consider the asymptotic behaviour of this process when the size
of the torus is taken to infinity and the overall rate of mutation tends t
o zero fast enough that mutations are sufficiently separated in time\, so
that the amount of time spent on configurations with more than one type be
comes negligible. We show that\, after a suitable projection (which extrac
ts just the dominant type from the configuration of individuals in the tor
us) and time scaling\, the process converges to a Markov jump process on t
he positive real lines\, whose rates we determine. Joint work with Adrián
González Casanova and András Tobias.\nSpeakers:\nDaniel Valesin (Univer
sity of Warwick)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/7453685b-814a-429b-884d-3ce4f01ad20e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limit of an adaptive contact process - Daniel Val
esin (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weaves\, webs and flows - Nic Freeman (University of Sheffield)
DTSTART;VALUE=DATE-TIME:20221017T120000
DTEND;VALUE=DATE-TIME:20221017T130000
UID:https://talks.ox.ac.uk/talks/id/28e9ca1a-e041-4284-9ccd-27ea487424fc/
DESCRIPTION:We consider "weaves" - loosely\, a weave is a set of non-cross
ing cadlag paths that covers 1+1 dimensional space-time. Here\, we do not
require any particular distribution for the particle motions. Weaves are a
general class of random processes\, of which the Brownian web is a canoni
cal example\; just as Brownian motion is a canonical example of a (single)
random path. It turns out that the space of weaves has an interesting geo
metric structure in its own right\, which will be the focus of the talk. T
his structure provides key information that leads to an accessible theory
of weak convergence for general weaves. Joint work with Jan Swart.\nSpeake
rs:\nNic Freeman (University of Sheffield)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/28e9ca1a-e041-4284-9ccd-27ea487424fc/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Weaves\, webs and flows - Nic Freeman (University of Shef
field)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Transitive closure in a polluted environment - Brett Kolesnik (Uni
versity of Oxford)
DTSTART;VALUE=DATE-TIME:20221010T120000
DTEND;VALUE=DATE-TIME:20221010T130000
UID:https://talks.ox.ac.uk/talks/id/1c42cc89-dd00-413c-82ce-300dbb4e3c60/
DESCRIPTION:We introduce a new percolation model\, inspired by recent work
s on jigsaw percolation\, graph bootstrap percolation\, and percolation in
polluted environments. We start with a collection of logical statements a
nd known implications\, as represented by an oriented graph G on n vertice
s. Then we attempt to logically complete the knowledge by transitivity\, h
owever\, a censor places restrictions\, represented by open and closed dir
ected edges. We show that if G is a connected graph of bounded degree\, an
d all other edges are open independently with probability p\, then the tra
nsition between sparse and full completion of open edges occurs at p_c = (
log n)^{-1/2+o(1)}. Joint work with Janko Gravner.\nSpeakers:\nBrett Koles
nik (University of Oxford)
LOCATION:Mathematical Institute (L1)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/1c42cc89-dd00-413c-82ce-300dbb4e3c60/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Transitive closure in a polluted environment - Brett Kole
snik (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limits of multi-type Markov Branching Trees - Robin Stephe
nson (University of Sheffield)
DTSTART;VALUE=DATE-TIME:20220216T120000Z
DTEND;VALUE=DATE-TIME:20220216T130000Z
UID:https://talks.ox.ac.uk/talks/id/b30df359-9194-458b-9d6c-e1f17ef941fd/
DESCRIPTION:Consider a population where individuals have two characteristi
cs: a size\, which is a positive integer\, and a type\, which is a member
of a finite set. This population reproduces in a Galton-Watson fashion\, w
ith one additional condition: given that an individual has size $n$\, the
sum of the sizes of its children is less than or equal to n. We call multi
-type Markov branching tree the family tree of such a population.\n\nWe sh
ow that under some assumptions about the splitting rates\, Markov branchin
g trees have scaling limits in distribution which are self-similar fragmen
tation trees\, monotype or multi-type.\n\nWe then give two applications: t
he scaling limits of some growth models of random trees\, and new results
on the scaling limits of multi-type Galton-Watson trees.\n\nThis is joint
work with Bénédicte Haas.\n\nSpeakers:\nRobin Stephenson (University of
Sheffield)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b30df359-9194-458b-9d6c-e1f17ef941fd/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limits of multi-type Markov Branching Trees - Rob
in Stephenson (University of Sheffield)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Local and global behavior of the subcritical contact process - Dr
Leonardo Rolla (University of Warwick)
DTSTART;VALUE=DATE-TIME:20220223T120000Z
DTEND;VALUE=DATE-TIME:20220223T130000Z
UID:https://talks.ox.ac.uk/talks/id/881d7822-7143-45d1-b982-2a6350e6efb4/
DESCRIPTION:We will describe the scaling limit of the subcritical contact
process in terms of a marked Poisson point process and a quasi-stationary
distribution\, and discuss the question of uniqueness of the QSD in this a
nd other contexts. Based on joint works with E. Andjel\, F. Ezanno and P.
Groisman\, with Aurelia Deshayes\, and with F. Arrejoría and P. Groisman.
\nSpeakers:\nDr Leonardo Rolla (University of Warwick)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/881d7822-7143-45d1-b982-2a6350e6efb4/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Local and global behavior of the subcritical contact proc
ess - Dr Leonardo Rolla (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Local and global behavior of the subcritical contact process - Dr
Leonardo Rolla (University of Warwick)
DTSTART;VALUE=DATE-TIME:20220223T120000Z
DTEND;VALUE=DATE-TIME:20220223T130000Z
UID:https://talks.ox.ac.uk/talks/id/881d7822-7143-45d1-b982-2a6350e6efb4/
DESCRIPTION:We will describe the scaling limit of the subcritical contact
process in terms of a marked Poisson point process and a quasi-stationary
distribution\, and discuss the question of uniqueness of the QSD in this a
nd other contexts. Based on joint works with E. Andjel\, F. Ezanno and P.
Groisman\, with Aurelia Deshayes\, and with F. Arrejoría and P. Groisman.
\nSpeakers:\nDr Leonardo Rolla (University of Warwick)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/881d7822-7143-45d1-b982-2a6350e6efb4/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Local and global behavior of the subcritical contact proc
ess - Dr Leonardo Rolla (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exchangeability\, mixtures and continuum random trees - Minmin Wan
g (University of Sussex)
DTSTART;VALUE=DATE-TIME:20220209T120000Z
DTEND;VALUE=DATE-TIME:20220209T130000Z
UID:https://talks.ox.ac.uk/talks/id/44d82120-1076-4284-8730-9bc70119368d/
DESCRIPTION:I’ll start with a quick review on some classical results on
exchangeability\, particularly Kallenberg’s theorem on the canonical for
m of an exchangeable process on [0\, 1]. The 2005 work of Aldous\, Miermon
t and Pitman reveals a close connection between exchangeable processes and
a class of continuum random tree called inhomogeneous continuum random tr
ees (ICRT)\, leading to their claim that Lévy trees are mixtures of ICRT.
I’ll present a proof in the case of stable Lévy trees\, based upon a
new way of constructing continuum random trees that work both for stable t
rees and ICRT.\nSpeakers:\nMinmin Wang (University of Sussex)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/44d82120-1076-4284-8730-9bc70119368d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Exchangeability\, mixtures and continuum random trees - M
inmin Wang (University of Sussex)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exchangeability\, mixtures and continuum random trees - Minmin Wan
g (University of Sussex)
DTSTART;VALUE=DATE-TIME:20220209T120000Z
DTEND;VALUE=DATE-TIME:20220209T130000Z
UID:https://talks.ox.ac.uk/talks/id/44d82120-1076-4284-8730-9bc70119368d/
DESCRIPTION:I’ll start with a quick review on some classical results on
exchangeability\, particularly Kallenberg’s theorem on the canonical for
m of an exchangeable process on [0\, 1]. The 2005 work of Aldous\, Miermon
t and Pitman reveals a close connection between exchangeable processes and
a class of continuum random tree called inhomogeneous continuum random tr
ees (ICRT)\, leading to their claim that Lévy trees are mixtures of ICRT.
I’ll present a proof in the case of stable Lévy trees\, based upon a
new way of constructing continuum random trees that work both for stable t
rees and ICRT.\nSpeakers:\nMinmin Wang (University of Sussex)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/44d82120-1076-4284-8730-9bc70119368d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Exchangeability\, mixtures and continuum random trees - M
inmin Wang (University of Sussex)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random walk on the simple symmetric exclusion process - Daniel Kio
us (University of Bath)
DTSTART;VALUE=DATE-TIME:20220126T120000Z
DTEND;VALUE=DATE-TIME:20220126T130000Z
UID:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
DESCRIPTION:In a joint work with Marcelo R. Hilário and Augusto Teixeira\
, we investigate the long-term behavior of a random walker evolving on top
of the simple symmetric exclusion process (SSEP) at equilibrium. At each
jump\, the random walker is subject to a drift that depends on whether it
is sitting on top of a particle or a hole. The asymptotic behavior is expe
cted to depend on the density ρ in [0\, 1] of the underlying SSEP.\nOur f
irst result is a law of large numbers (LLN) for the random walker for all
densities ρ except for at most two values ρ− and ρ+ in [0\, 1]\, wher
e the speed (as a function of the density) possibly jumps from\, or to\, 0
. \nSecond\, we prove that\, for any density corresponding to a non-zero s
peed regime\, the fluctuations are diffusive and a Central Limit Theorem h
olds.\nFor the special case in which the density is 1/2 and the jump distr
ibution on an empty site and on an occupied site are symmetric to each oth
er\, we prove a LLN with zero limiting speed.\nOur main results extend to
environments given by a family of independent simple symmetric random walk
s in equilibrium.\nSpeakers:\nDaniel Kious (University of Bath)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Random walk on the simple symmetric exclusion process - D
aniel Kious (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random walk on the simple symmetric exclusion process - Daniel Kio
us (University of Bath)
DTSTART;VALUE=DATE-TIME:20220126T120000Z
DTEND;VALUE=DATE-TIME:20220126T130000Z
UID:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
DESCRIPTION:In a joint work with Marcelo R. Hilário and Augusto Teixeira\
, we investigate the long-term behavior of a random walker evolving on top
of the simple symmetric exclusion process (SSEP) at equilibrium. At each
jump\, the random walker is subject to a drift that depends on whether it
is sitting on top of a particle or a hole. The asymptotic behavior is expe
cted to depend on the density ρ in [0\, 1] of the underlying SSEP.\nOur f
irst result is a law of large numbers (LLN) for the random walker for all
densities ρ except for at most two values ρ− and ρ+ in [0\, 1]\, wher
e the speed (as a function of the density) possibly jumps from\, or to\, 0
. \nSecond\, we prove that\, for any density corresponding to a non-zero s
peed regime\, the fluctuations are diffusive and a Central Limit Theorem h
olds.\nFor the special case in which the density is 1/2 and the jump distr
ibution on an empty site and on an occupied site are symmetric to each oth
er\, we prove a LLN with zero limiting speed.\nOur main results extend to
environments given by a family of independent simple symmetric random walk
s in equilibrium.\nSpeakers:\nDaniel Kious (University of Bath)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Random walk on the simple symmetric exclusion process - D
aniel Kious (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limits of finitely specified permutation classes - Mickaë
l Maazoun (ENS Lyon)
DTSTART;VALUE=DATE-TIME:20200217T120000Z
DTEND;VALUE=DATE-TIME:20200217T130000Z
UID:https://talks.ox.ac.uk/talks/id/76cda1bb-51ad-46c2-9b2d-e34ba488e0d4/
DESCRIPTION:The subject of pattern-avoiding permutations is a classic of e
numerative combinatorics\, still rich of interesting open problems. We ado
pt a probabilistic point of view: What does the diagram of a large permuta
tion in a pattern-avoiding class typically look like? Generalising previo
us results\, we consider classes with nice encodings by multi-type trees.
We show that they converge either to "Brownian separable permutons" or det
erministic limit shapes.\n\nI will explain how we use analytic combinatori
cs to study the scaling limit of the encoding trees without completely los
ing information about types and degrees of branch points.\n\nIf I have som
e time left\, I will talk about some computations that we can perform on t
he limiting objects\, with interesting consequences in the discrete.\n\nTh
is is joint work with F. Bassino\, M. Bouvel\, V. Féray\, L. Gerin\, A. P
ierrot -- arXiv:1903.07522.\nSpeakers:\nMickaël Maazoun (ENS Lyon)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/76cda1bb-51ad-46c2-9b2d-e34ba488e0d4/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limits of finitely specified permutation classes
- Mickaël Maazoun (ENS Lyon)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:The depth first search exploration of a supercritical configuratio
n model - Laurent Ménard (Université Paris Nanterre)
DTSTART;VALUE=DATE-TIME:20191121T100000Z
DTEND;VALUE=DATE-TIME:20191121T110000Z
UID:https://talks.ox.ac.uk/talks/id/b99e823e-182d-4f5e-88be-387c8632ce72/
DESCRIPTION:We consider large random graphs with a given degree sequence.
In the sparse regime where the degree sequence converges to a probability
distribution\, the model has a phase transition for the existence of a mac
roscopic connected component. In this talk\, we will study the depth first
search algorithm in the supercritical regime. In particular\, we will see
that the evolution of the empirical degree distribution of the unexplored
vertices has a fluid limit which is driven by an infinite system of diffe
rential equations. Surprisingly\, this system admits an explicit solution
in terms of the initial degree distribution. This in turn allows to prove
that the renormalised contour process of the exploration has a determinist
ic profile for which we can give an explicit parametric representation. Th
e height of this curve gives information about long simple paths in the gr
aph.\nSpeakers:\nLaurent Ménard (Université Paris Nanterre)
LOCATION:24-29 St Giles' (Department of Statistics\, LG.01 (Large Lecture
Theatre))\, 24-29 St Giles' OX1 3LB
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b99e823e-182d-4f5e-88be-387c8632ce72/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The depth first search exploration of a supercritical con
figuration model - Laurent Ménard (Université Paris Nanterre)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Where are the faraway particles of the branching Brownian motion i
n dimension d? - Roman Stasiński (Department of Statistics\, University o
f Oxford)
DTSTART;VALUE=DATE-TIME:20191125T120000Z
DTEND;VALUE=DATE-TIME:20191125T130000Z
UID:https://talks.ox.ac.uk/talks/id/963053ca-f60f-46cd-b218-fde0b846d6d5/
DESCRIPTION:Branching Brownian motion is a model in which independent part
icles move as Brownian motions and branch at rate 1. Its behavior\, and in
particular the description of what happens near its extremal particles (t
he ones furthest away from the origin) is by now well understood in\ndimen
sion 1. By contrast\, not much is known about the multidimensional case.\n
\nIn this talk I will present the first step towards the goal of obtaining
the limiting extremal point process for the branching Brownian motion in\
nhigher dimensions. This involves in particular finding an analogue of the
so-called derivative martingale\, which plays a crucial role in d=1\,\nan
d studying its convergence.\n \nBased on a joint work with Bastien Mallein
(Université Paris 13).\nSpeakers:\nRoman Stasiński (Department of Stati
stics\, University of Oxford)
LOCATION:L4
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/963053ca-f60f-46cd-b218-fde0b846d6d5/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Where are the faraway particles of the branching Brownian
motion in dimension d? - Roman Stasiński (Department of Statistics\, Uni
versity of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Critical scaling limit of the random intersection graph -- POSTPON
ED TO NEXT TERM - Lorenzo Federico (University of Warwick)
DTSTART;VALUE=DATE-TIME:20191125T120000Z
DTEND;VALUE=DATE-TIME:20191125T130000Z
UID:https://talks.ox.ac.uk/talks/id/e8763c31-3d03-442d-b26f-a6d471576a7e/
DESCRIPTION:\nStatus: This talk has been cancelled\nIn this talk\, we prov
e a scaling limit for the size (both in terms of vertices and edges) of th
e largest components of a critical random intersection graph in which each
individual is assigned to each community with a uniform probability p\, a
ll independently of each other. We show that the order of magnitude of the
largest component depends significantly on the asymptotic behaviour of th
e ratio between the number of individuals and communities\, while the limi
t random variables to which component sizes converge after rescaling are t
he same as in the Erdos-Renyi Random Graph. We further discuss how this re
sult relates to the known scaling limits of critical inhomogeneous random
graphs.\nSpeakers:\nLorenzo Federico (University of Warwick)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e8763c31-3d03-442d-b26f-a6d471576a7e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Critical scaling limit of the random intersection graph -
- POSTPONED TO NEXT TERM - Lorenzo Federico (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asymptotics of discrete β-corners processes via discrete loop equ
ations - Alisa Knizel (Columbia University\, New York)
DTSTART;VALUE=DATE-TIME:20191104T120000Z
DTEND;VALUE=DATE-TIME:20191104T130000Z
UID:https://talks.ox.ac.uk/talks/id/357d7fce-9664-4aef-92eb-6127c8aa2c79/
DESCRIPTION:We introduce and study stochastic particle ensembles which are
natural discretizations of general β-corners processes. We prove that un
der technical assumptions on a general analytic potential the global fluct
uations for the difference between two adjacent levels are asymptotically
Gaussian. The covariance is universal and remarkably differs from its coun
terpart in random matrix theory. Our main tools are certain novel algebrai
c identities that are multi-level analogues of the discrete loop equations
. Based on joint work with Evgeni Dimitrov (Columbia University)\nSpeakers
:\nAlisa Knizel (Columbia University\, New York)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/357d7fce-9664-4aef-92eb-6127c8aa2c79/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Asymptotics of discrete β-corners processes via discrete
loop equations - Alisa Knizel (Columbia University\, New York)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exceptional times of transience for a dynamical random walk - Matt
hew Roberts (University of Bath)
DTSTART;VALUE=DATE-TIME:20191028T120000Z
DTEND;VALUE=DATE-TIME:20191028T130000Z
UID:https://talks.ox.ac.uk/talks/id/30ad2bdb-e190-4cae-924d-3f2848081495/
DESCRIPTION:We define a dynamical simple symmetric random walk in one dime
nsion\, and show that there almost surely exist exceptional times at which
the walk tends to infinity. In fact the set of such times has Hausdorff d
imension 1/2 almost surely. This is in contrast to the usual dynamical sim
ple symmetric random walk in one dimension\, for which such exceptional ti
mes are known not to exist. This is joint work with Martin Prigent.\nSpeak
ers:\nMatthew Roberts (University of Bath)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/30ad2bdb-e190-4cae-924d-3f2848081495/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Exceptional times of transience for a dynamical random wa
lk - Matthew Roberts (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Order of the variance in the discrete Hammersley process - Nicos G
eorgiou (University of Sussex)
DTSTART;VALUE=DATE-TIME:20191118T120000Z
DTEND;VALUE=DATE-TIME:20191118T130000Z
UID:https://talks.ox.ac.uk/talks/id/546181e7-31a9-4197-b8a7-58a5163e7e59/
DESCRIPTION:We discuss the order of the variance on a lattice analogue of
the Hammersley process\, for which the environment on each site has indepe
ndent\, Bernoulli distributed values. The last passage time is the maximu
m number of Bernoulli points that can be collected on a piecewise linear p
ath\, where each segment has strictly positive but finite slope.\n\nFor th
is model the shape function exhibits two flat edges and we study the order
of the variance in directions that fall in the flat edge\, in directions
that approximate the edge of the flat edge\, and in directions in the stri
ctly concave section of the shape for the i.i.d. model and for the associa
ted equilibrium model with boundaries. If time permitting\, we will discu
ss the shape function and variance in some inhomogeneous models as well. \
n\nThis is an exposition of several works with Janosch Ortmann\, Elnur Emr
ah and Federico Ciech.\nSpeakers:\nNicos Georgiou (University of Sussex)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/546181e7-31a9-4197-b8a7-58a5163e7e59/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Order of the variance in the discrete Hammersley process
- Nicos Georgiou (University of Sussex)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sparse graphs using exchangeable random measures: Models\, propert
ies and applications - François Caron (Department of Statistics\, Univers
ity of Oxford)
DTSTART;VALUE=DATE-TIME:20191111T120000Z
DTEND;VALUE=DATE-TIME:20191111T130000Z
UID:https://talks.ox.ac.uk/talks/id/f9f19da2-620c-4a5e-9fe6-211327a00b7e/
DESCRIPTION:In the talk I will present the class of random graphs based on
exchangeable random measures. Such class allows to model networks which a
re either dense or sparse\, that is where the number of edges scales subqu
adratically with the number of nodes. For some values of its parameters\,
it generates scale-free networks with power-law exponent between 1 and 2.
I will present the general construction\, a representation theorem for suc
h construction due to Kallenberg\, and discuss its sparsity\, power-law an
d transitivity properties. Then I will introduce a specific model within t
his framework that allows to capture sparsity/heavy-tailed degree distribu
tions as well as latent overlapping community structure\, and a Markov cha
in Monte Carlo algorithm for posterior inference with this model. Experime
nts are done on two real-world networks\, showing the usefulness of the ap
proach for network analysis. \n\nBased on joint work with Emily Fox\, Adri
en Todeschini\, Xenia Miscouridou\, Judith Rousseau\, Francesca Panero.\nS
peakers:\nFrançois Caron (Department of Statistics\, University of Oxford
)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/f9f19da2-620c-4a5e-9fe6-211327a00b7e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Sparse graphs using exchangeable random measures: Models\
, properties and applications - François Caron (Department of Statistics\
, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hit and miss with the density of the (α\,β)-superprocess - Thoma
s Hughes (UBC)
DTSTART;VALUE=DATE-TIME:20191014T120000
DTEND;VALUE=DATE-TIME:20191014T130000
UID:https://talks.ox.ac.uk/talks/id/6c1fbe4e-7273-4fd6-a429-277d47f57ade/
DESCRIPTION:The (α\,β)-superprocess is a spatial branching model associa
ted to an α-stable spatial motion and a (1+β)-stable branching mechanism
. Formally\, it is a measure-valued Markov process\, but this talk concer
ns the absolutely continuous parameter regime\, in which the random measur
e has a density. After introducing this process and some classical results
\, I will discuss some newly proven path properties of the density. These
include (i) strict positivity of the density at a fixed time (for certain
values of α and β) and (ii) a classification of the measures which the d
ensity “charges” almost surely\, and of the measures which the density
fails to charge with positive probability\, when conditioned on survival.
The duality between the superprocess and a fractional PDE is central to o
ur method\, and I will discuss how the probabilistic statements above corr
espond to new results about solutions to the PDE.\n\nSpeakers:\nThomas Hug
hes (UBC)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/6c1fbe4e-7273-4fd6-a429-277d47f57ade/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Hit and miss with the density of the (α\,β)-superproces
s - Thomas Hughes (UBC)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anchored expansion in supercritical percolation on nonamenable gra
phs - Jonathan Hermon (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20190507T120000
DTEND;VALUE=DATE-TIME:20190507T130000
UID:https://talks.ox.ac.uk/talks/id/1fa9bea7-0fa5-4981-a842-26111ed1dcba/
DESCRIPTION:Let G be a transitive nonamenable graph\, and consider supercr
itical Bernoulli bond percolation on G. We prove that the probability that
the origin lies in a finite cluster of size n decays exponentially in n.
We deduce that: \n\n1. Every infinite cluster has anchored expansion almos
t surely. This answers positively a question of Benjamini\, Lyons\, and Sc
hramm (1997). \n\n2. Various observables\, including the percolation proba
bility and the truncated susceptibility are analytic functions of p throug
hout the entire supercritical phase.\n\nJoint work with Tom Hutchcroft. \n
Speakers:\nJonathan Hermon (University of Cambridge)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/1fa9bea7-0fa5-4981-a842-26111ed1dcba/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Anchored expansion in supercritical percolation on noname
nable graphs - Jonathan Hermon (University of Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universal vanishing corrections on the position of fronts in the F
isher-KPP class - Éric Brunet (Laboratoire de Physique Statistique\, ENS
Paris)
DTSTART;VALUE=DATE-TIME:20190429T120000
DTEND;VALUE=DATE-TIME:20190429T130000
UID:https://talks.ox.ac.uk/talks/id/97b4a567-7908-43e9-b2d2-800f032df33d/
DESCRIPTION:The distribution function of the rightmost particle in a branc
hing Brownian \nmotion satisfies the Fisher-KPP equation:\n\n∂u/∂t =
∂²u/∂x² + u - u²\n\nSuch an equation appears also in biology\, chem
istry or theoretical physics\nto describe a moving interface\, or a front\
, between a stable and an unstable \nmedium.\n\nThirty years ago\, Bramson
gave rigorous sharp estimates on the position of \nthe front\, and\, fift
een years ago\, Ebert and van Saarloos heuristically \nidentified universa
l vanishing corrections.\n\nIn this presentation\, I will present a novel
way to study the position of \nsuch a front\, which allows to recover all
the known terms and find some new \nones. We start by studying a front equ
ation where the non-linearity is \nreplaced by a condition at a free bound
ary\, and we show how to extend our \nresults to the actual Fisher-KPP.\nS
peakers:\nÉric Brunet (Laboratoire de Physique Statistique\, ENS Paris)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/97b4a567-7908-43e9-b2d2-800f032df33d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Universal vanishing corrections on the position of fronts
in the Fisher-KPP class - Éric Brunet (Laboratoire de Physique Statistiq
ue\, ENS Paris)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Infinitely ramified point measure and branching Lévy process - Ba
stien Mallein (Paris 13)
DTSTART;VALUE=DATE-TIME:20190128T120000Z
DTEND;VALUE=DATE-TIME:20190128T130000Z
UID:https://talks.ox.ac.uk/talks/id/e7aeb00f-87c1-41cd-ad2c-17605c7afe44/
DESCRIPTION:An infinitely ramified point measure is a random point measure
that can be written as the terminal value of a branching random walk of a
ny length. This is the equivalent\, in branching processes theory\, to the
notion of infinitely divisible random variables for real-valued random va
riables. In this talk\, we show a connexion between infinitely ramified po
int measures and branching Lévy processes\, a continuous-time particle sy
stem on the real line\, in which particles move according to independent L
évy processes\, and give birth to children in a Poisson fashion.\n\nSpeak
ers:\nBastien Mallein (Paris 13)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e7aeb00f-87c1-41cd-ad2c-17605c7afe44/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Infinitely ramified point measure and branching Lévy pro
cess - Bastien Mallein (Paris 13)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:U-statistics: some old and new results with applications to patter
ns in random strings and permutations - Svante Janson (Uppsala University)
DTSTART;VALUE=DATE-TIME:20190211T120000Z
DTEND;VALUE=DATE-TIME:20190211T130000Z
UID:https://talks.ox.ac.uk/talks/id/b9bbf382-7e7c-4f21-9642-b9f5c70e3ce8/
DESCRIPTION:U-statistics form a large class of random variables that appea
r in many contexts. I will focus on some simple and some less obvious appl
ications to patterns in random permutations and random strings\, and gener
al results useful in these applications (and sometimes motivated by them).
This will include some less common versions of U-statistics (asymmetric U
-statistics and U-statistics based on an m-dependent sequence)\, and some
new results on renewal theory for U-statistics.\nSpeakers:\nSvante Janson
(Uppsala University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b9bbf382-7e7c-4f21-9642-b9f5c70e3ce8/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:U-statistics: some old and new results with applications
to patterns in random strings and permutations - Svante Janson (Uppsala Un
iversity)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orderings of Gibbs random samples - Yuri Yakubovich (St Petersburg
State University)
DTSTART;VALUE=DATE-TIME:20190121T120000Z
DTEND;VALUE=DATE-TIME:20190121T130000Z
UID:https://talks.ox.ac.uk/talks/id/3caadf9c-f9b7-43b3-9f75-18c738f6423e/
DESCRIPTION:Random partitions of finite sets play a key role in modelling
genetic diversity. The basic problem is to draw statistical inference abo
ut the general population where a sample partition on species is only obse
rvable. Mathematical models are greatly simplified by assuming that the po
pulation itself is a sample from an idealized infinite population\, due to
Kingman’s theory of exchangeable random partitions of countable sets\,
whereby partitions are modelled by sampling from a random discrete distrib
ution. In population genetics\, the sample values may carry additional cha
racteristics of the species. For example\, in Moran’s model with infinit
ely many alleles\, such a characteristic encodes the relative age of speci
es\, and the question of interest is\, given the observed frequencies of s
pecies in the sample\, to order them by age. Donnelly & Tavaré (1986) pro
ved that in the GEM(θ) model (which leads to the famous Ewens sampling fo
rmula)\, the distribution of the order by age is the same as that of the o
rder by appearance. In my talk\, I will show that in a two-parametric gene
ralization of the GEM model\, and more generally\, under the so-called Gib
bs sampling\, these two orders have different distributions which are neve
rtheless connected via a modification of the stochastic procedure known as
size-biased ordering.\nThis is joint work with Jim Pitman (Berkeley)\, do
i:10.1214/17-EJP59\; doi:10.1214/17-ECP95.\nSpeakers:\nYuri Yakubovich (St
Petersburg State University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/3caadf9c-f9b7-43b3-9f75-18c738f6423e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Orderings of Gibbs random samples - Yuri Yakubovich (St P
etersburg State University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Particle systems and systemic risk - Ben Hambly (University of Oxf
ord)
DTSTART;VALUE=DATE-TIME:20190114T120000Z
DTEND;VALUE=DATE-TIME:20190114T130000Z
UID:https://talks.ox.ac.uk/talks/id/925fb523-8dcd-4aae-871e-d325a1dccd82/
DESCRIPTION:Systemic risk in the banking system is the risk that small los
ses and defaults can escalate through endogenous effects to cause an event
affecting large parts of the financial sector. We will consider some simp
le particle system models for the interactions between banks and show how
this leads to stochastic McKean-Vlasov equations describing the whole syst
em. The systemic risk can be captured through a loss function and we will
show that this can have unexpected behaviour in different models.\nSpeaker
s:\nBen Hambly (University of Oxford)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/925fb523-8dcd-4aae-871e-d325a1dccd82/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Particle systems and systemic risk - Ben Hambly (Universi
ty of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polynomial mixing time for edge flips on quadrangulations - Alessa
ndra Caraceni (University of Bath)
DTSTART;VALUE=DATE-TIME:20181119T120000Z
DTEND;VALUE=DATE-TIME:20181119T130000Z
UID:https://talks.ox.ac.uk/talks/id/46c81587-5db3-4968-9702-2e7f69e098b7/
DESCRIPTION:This talk will revolve around recent joint work with Alexandre
Stauffer in which we give the first polynomial upper bound for the relaxa
tion time of the edge flip Markov chain on rooted quadrangulations. A quad
rangulation of size n is a connected planar graph endowed with a cellular
embedding in the sphere such that all of its n faces have degree 4\, consi
dered up to orientation-preserving homeomorphisms of the sphere itself\; w
e call it rooted when it is endowed with a distinguished oriented edge. Gi
ven a (rooted) quadrangulation of size n\, a step of the Markov chain we a
re interested in – a so-called “edge flip” – consists in choosing
an edge uniformly at random\, deleting it and replacing it with one of the
three possible edges (two when the original edge is adjacent to only one
face) which\, if drawn\, recreate a quadrangulation. We will see how one c
an relate the edge flip chain on quadrangulations to a “leaf translation
” chain on plane trees (which has a natural interpretation as a chain on
the set of Dyck paths\, and on other Catalan structures as well). Having
discussed how to set up a successful comparison between the two chains whi
ch exploits the well-known bijection by Schaeffer and a specific construct
ion of leaf translations as sequences of edge flips\, we shall estimate th
e relaxation time of the leaf translation chain\, thereby improving on a r
esult by Movassagh and Shor.\nSpeakers:\nAlessandra Caraceni (University o
f Bath)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/46c81587-5db3-4968-9702-2e7f69e098b7/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Polynomial mixing time for edge flips on quadrangulations
- Alessandra Caraceni (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Branching Brownian motion with decay of mass and the non-local Fis
her-KPP equation - Julien Berestycki (University of Oxford)
DTSTART;VALUE=DATE-TIME:20181105T120000Z
DTEND;VALUE=DATE-TIME:20181105T130000Z
UID:https://talks.ox.ac.uk/talks/id/9ffb5852-ff86-4773-842d-d7849d33538e/
DESCRIPTION:The non-local variant of the celebrated Fisher-KPP equation de
scribes the growth and spread of population in which individuals diffuse\,
reproduce and - crucially - interact through a non-local competition mech
anism. This type of equation is intrinsically harder to study than the cla
ssical Fisher-KPP equation because we lose such powerful tools as the comp
arison principle and the maximum principle. In this talk\, I will show how
this equation arises as the hydrodynamic limit of a particle system -the
branching Brownian motion with decay of mass\, and use this to study front
propagation behaviours.\n\nThis is based on joint work with Louigi Addari
o-Berry and Sarah Penington.\nSpeakers:\nJulien Berestycki (University of
Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/9ffb5852-ff86-4773-842d-d7849d33538e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Branching Brownian motion with decay of mass and the non-
local Fisher-KPP equation - Julien Berestycki (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Where do second class particles walk? - Márton Balázs (Universit
y of Bristol)
DTSTART;VALUE=DATE-TIME:20181022T120000
DTEND;VALUE=DATE-TIME:20181022T130000
UID:https://talks.ox.ac.uk/talks/id/e7dc4443-a2dd-4dbf-867d-c910db5ad4b5/
DESCRIPTION:I will tell about a long story in interacting particle systems
that emerged across decades in several stages:\n\n1. A second class parti
cle in asymmetric exclusion (ASEP) and in an exponential bricklayers proce
ss (EBPL) sees certain shock-like distributions stationary.\n\n2. Such sho
ck-like distributions perform a simple random walk in both ASEP and EBLP (
what does that mean...?)\n\n3. It is in fact the second class particle in
the middle of the shock that does the random walk (what does THIS mean...?
). Besides ASEP and EBLP\, it also works for an exponential zero range pro
cess (EZRP).\n\n4. Q-zero range is yet another example that has this rando
m walking property. The second class particle really helps to reveal this
secret here.\n\nThe last step is recent\, the ones before are old results.
\n\n(Joint work with Gyorgy Farkas\, Peter Kovacs\, Attila Rakos\; Lewis D
uffy\, Dimitri Pantelli)\nSpeakers:\nMárton Balázs (University of Bristo
l)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e7dc4443-a2dd-4dbf-867d-c910db5ad4b5/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Where do second class particles walk? - Márton Balázs (
University of Bristol)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamics of limit order books: queueing models\, diffusion limits
and stochastic PDEs - Rama Cont (University of Oxford)
DTSTART;VALUE=DATE-TIME:20181015T120000
DTEND;VALUE=DATE-TIME:20181015T130000
UID:https://talks.ox.ac.uk/talks/id/d1074e46-233c-45a6-a47d-8a1b2db1de15/
DESCRIPTION:The advent of electronic trading in financial markets has led
to a market landscape in which buyers and sellers by submitting orders thr
ough a central limit order book\, where orders are matched and executed a
ccording to time and price priority. The wide range of frequencies involve
d - from microseconds to days - requires a consistent description of mark
et dynamics across time scales.\n\nBased on a detailed empirical study of
high frequency order flow in equity and futures markets\, we propose a mul
ti-scale stochastic model for dynamics of price and order flow in a limit
order market\, which captures the coexistence of high frequency and low fr
equency order flow and examines the consequences of this heterogeneity on
intraday price dynamics\, volatility and liquidity.\n\nWe then use probabi
listic limit theorems to derive the dynamics of the order book and market
price at various time scales. \nStarting from a description of the order b
ook as a multi-class spatial queueing system at the highest (micro- or mi
lli-second) frequency\, we show that over intermediate time scales -- sec
onds -- the dynamics of the active queues may be described as a diffusion
in a wedge with discontinuous reflection at the boundary\, while the marke
t price follows a jump process driven by the boundary local time of this d
iffusion.\n\nOver longer time scales\, the effective dynamics of the order
book may be described as a stochastic moving boundary problem while the
market price follows a diffusion in a random environment defined by the or
der book. We will emphasise how asymptotics across time scales provides in
sights into the relations between supply\, demand\, liquidity and volatili
ty in limit order markets.\nSpeakers:\nRama Cont (University of Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d1074e46-233c-45a6-a47d-8a1b2db1de15/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Dynamics of limit order books: queueing models\, diffusi
on limits and stochastic PDEs - Rama Cont (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Metastable behaviour of the dilute Curie-Weiss model - Martin Slow
ik (TU Berlin)
DTSTART;VALUE=DATE-TIME:20181126T120000Z
DTEND;VALUE=DATE-TIME:20181126T130000Z
UID:https://talks.ox.ac.uk/talks/id/d9912ad8-b9b5-4123-a72d-d6a53ad4903b/
DESCRIPTION:Metastability is a phenomenon that occurs in the dynamics of a
multi-stable non-linear system subject to noise. It is characterized by
the existence of multiple\, well separated time scales. The talk will be
focus on the metastable behavior of the dilute Curie-Weiss model\, that is
a Ising spin system on a Erdos-Renyi random graph with $N$ vertices and r
etention probability $p \\in (0\,1)$. Each spin interacts with a external
field\, while the interaction among neighbouring spin variables is assumed
to be of the same strength. In particular\, I will discuss bounds on the
mean exit time from the metastable to the stable state and the spectral g
ap.\n\n \nSpeakers:\nMartin Slowik (TU Berlin)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d9912ad8-b9b5-4123-a72d-d6a53ad4903b/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Metastable behaviour of the dilute Curie-Weiss model - Ma
rtin Slowik (TU Berlin)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algorithmic Pirogov-Sinai Theory - Tyler Helmuth (University of Br
istol)
DTSTART;VALUE=DATE-TIME:20181112T120000Z
DTEND;VALUE=DATE-TIME:20181112T130000Z
UID:https://talks.ox.ac.uk/talks/id/8558c060-74a2-4acd-a1de-9407263e6492/
DESCRIPTION:The hard-core model is a basic and important model in statisti
cal mechanics\, probability\, and theoretical computer science. I’ll int
roduce the model\, and after describing some known algorithmic results\, w
ill discuss a polynomial-time algorithm for approximately sampling from th
e hard-core model at high densities on the integer lattices. This is the r
egime in which the Glauber dynamics are known to mix exponentially slowly.
Our algorithm relies in an essential way on Pirogov-Sinai theory\, an imp
ortant tool for understanding the phase diagram of high-density discrete s
tatistical mechanics models. \n\nThis is joint work with Will Perkins and
Guus Regts.\nSpeakers:\nTyler Helmuth (University of Bristol)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/8558c060-74a2-4acd-a1de-9407263e6492/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Algorithmic Pirogov-Sinai Theory - Tyler Helmuth (Univers
ity of Bristol)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finding cliques using few probes - Miklós Rácz (Princeton Unive
rsity)
DTSTART;VALUE=DATE-TIME:20181029T120000Z
DTEND;VALUE=DATE-TIME:20181029T130000Z
UID:https://talks.ox.ac.uk/talks/id/e96d4efd-c944-4dd3-8684-25f1eba6b948/
DESCRIPTION:I will talk about algorithms (with unlimited computational pow
er) which adaptively probe pairs of vertices of a graph to learn the prese
nce or absence of edges and whose goal is to output a large clique. I will
focus on the case of the random graph G(n\,1/2)\, in which case the size
of the largest clique is roughly 2\\log(n). Our main result shows that if
the number of pairs queried is linear in n and adaptivity is restricted to
finitely many rounds\, then the largest clique cannot be found\; more pre
cisely\, no algorithm can find a clique larger than c\\log(n) where c < 2
is an explicit constant. This is joint work with Uriel Feige\, David Gamar
nik\, Joe Neeman\, and Prasad Tetali. \nSpeakers:\nMiklós Rácz (Princeto
n University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e96d4efd-c944-4dd3-8684-25f1eba6b948/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Finding cliques using few probes - Miklós Rácz (Prince
ton University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limits of (randomly) growing Schröder trees and exchangeability -
Julian Gerstenberg (Leibniz Universität Hannover)
DTSTART;VALUE=DATE-TIME:20181008T120000
DTEND;VALUE=DATE-TIME:20181008T130000
UID:https://talks.ox.ac.uk/talks/id/16131e1b-de82-4227-ad4a-ab46c536a9a0/
DESCRIPTION:We consider finite rooted ordered trees in which every interna
l node has at least two children\, sometimes called Schröder trees\; the
size |t| of such a tree t is the number of its leaves. An important concep
t with trees is that of inducing subtrees. Given a tree t of size k and a
larger tree t' of size n\\geq k we define 0 \\leq \\theta(t\,t')\\leq 1 to
be the probability of obtaining t as a randomly induced subtree of size k
in t'. One can think of \\theta(t\,t') to be the _density of the pattern
t in t'_. In this talk we consider two closely related questions concernin
g the nature of \\theta:\n1. A sequences of trees (t_n)_n with |t_n|\\righ
tarrow\\infty is called \\theta-convergent\, if \\theta(t\,t_n) converges
for every fixed tree t. The limit of (t_n)_n is the function t\\mapsto \\l
im_n\\theta(t\,t_n). What limits exist? \n2. A Markov chain (X_n)_n with X
_n being a random tree of size n is called a \\theta-chain if P(X_k=t|X_n=
t')=\\theta(t\,t') for all k \\leq n. What \\theta-chains exist?\n\nSimila
r questions have been treated for many different types of discrete structu
res (words\, permutations\, graphs \\dots)\; binary Schröder trees (Catal
an trees) are considered in [1]. We present a De Finetti-type representati
on for \\theta-chains and a homeomorphic description of limits of \\theta-
convergent sequences involving certain tree-like compact subsets of the sq
uare [0\,1]^2. Questions and results are closely linked to the study of ex
changeable hierarchies\, see [2]. \n\n[1] Evans\, Grübel and Wakolbinger.
"Doob-Martin boundary of Rémy's tree growth chain". The Annals of Probab
ility\, 2017.\n[2] Forman\, Haulk and Pitman. "A representation of exchang
eable hierarchies by sampling from random real trees". Prob.Theory and rel
ated Fields\, 2017.\n[3] Gerstenberg. "Exchangeable interval hypergraphs a
nd limits of ordered discrete structures". arXiv\, 2018.\nSpeakers:\nJulia
n Gerstenberg (Leibniz Universität Hannover)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/16131e1b-de82-4227-ad4a-ab46c536a9a0/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Limits of (randomly) growing Schröder trees and exchange
ability - Julian Gerstenberg (Leibniz Universität Hannover)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continuous-state branching process with dependent immigration - Ze
nghu Li (Beijing Normal University)
DTSTART;VALUE=DATE-TIME:20180606T120000
DTEND;VALUE=DATE-TIME:20180606T130000
UID:https://talks.ox.ac.uk/talks/id/bb91ed75-e520-4ac7-8099-ab1e76c74173/
DESCRIPTION:We are interested in a population model called continuous-stat
e branching process with dependent immigration (CBDI-processes). The immig
ration rate of the model depends on the current population size via a func
tion that can be non-Lipschitz. We give a construction of the process usin
g a stochastic equation driven by Poisson point measures on some path spac
es. This approach gives a direct construction of the sample path of the pr
ocess with general branching and immigration mechanisms from those of the
corresponding CB-process without immigration. By choosing the ingredients
suitably\, we can get either a new CB-process with different branching mec
hanism or a branching model with competition. We focus on the one-dimensio
nal model\, but the arguments carry over to the measure-valued setting. Th
ese kinds of constructions have been proved useful for the study of some f
inancial problems.\nSpeakers:\nZenghu Li (Beijing Normal University)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/bb91ed75-e520-4ac7-8099-ab1e76c74173/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Continuous-state branching process with dependent immigra
tion - Zenghu Li (Beijing Normal University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:High-density hard-core configurations on a triangular lattice - Yu
ri Suhov (Penn State and Cambridge)
DTSTART;VALUE=DATE-TIME:20180601T120000
DTEND;VALUE=DATE-TIME:20180601T130000
UID:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
DESCRIPTION:The high-density hard-core configuration model has attracted a
ttention for quite a long time. The first rigorous results about the phase
transition on a lattice with a nearest-neighbor exclusion where published
by Dobrushin in 1968. In 1979\, Baxter calculated the free energy and spe
cified the critical point on a triangular lattice with a nearest-neighbor
exclusion\; in 1980 Andrews gave a rigorous proof of Baxter's calculation
with the help of Ramanujan's identities. On a square lattice the nearest-n
eighbor exclusion critical point has been estimated from above and below i
n a series by a number of authors.\n\nWe analyze the hard-core model on a
triangular lattice and identify the extreme Gibbs measures (pure phases) f
or high densities. Depending on arithmetic properties of the hard-core dia
meter $D$\, the number of pure phases equals either $D^2$ or $2D^2$. A cla
ssification of possible cases can be given in terms of Eisenstein primes.\
n\nIf the time allows\, I will mention 3D analogs of some of these results
.\n\nThis is a joint work with A Mazel and I Stuhl\; cf. arXiv:1803.04041.
No special knowledge will be assumed from the audience.\n\n\nSpeakers:\nY
uri Suhov (Penn State and Cambridge)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:High-density hard-core configurations on a triangular lat
tice - Yuri Suhov (Penn State and Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the number of arithmetic progressions in sparse random sets - C
hristoph Koch (Department of Statistics\, University of Oxford)
DTSTART;VALUE=DATE-TIME:20180423T120000
DTEND;VALUE=DATE-TIME:20180423T130000
UID:https://talks.ox.ac.uk/talks/id/50cd5e62-d126-4531-a276-f7ed5417f890/
DESCRIPTION:We study arithmetic progressions $\\{a\,a+b\,a+2b\,\\dots\,a+(
\\ell-1) b\\}$\, with $\\ell\\ge 3$\, in random subsets of the initial seg
ment of natural numbers $[n]:=\\{1\,2\,\\dots\, n\\}$. Given $p\\in[0\,1]$
we denote by $[n]_p$ the random subset of $[n]$ which includes every numb
er with probability $p$\, independently of one another. The focus lies on
sparse random subsets\, i.e.\\ when $p=p(n)=o(1)$ with respect to $n\\to\\
infty$.\n\nLet $X_\\ell$ denote the number of distinct arithmetic progress
ions of length $\\ell$ which are contained in $[n]_p$. We determine the li
miting distribution for $X_\\ell$ not only for fixed $\\ell\\ge 3$ but als
o when $\\ell=\\ell(n)\\to\\infty$ sufficiently slowly. Moreover\, we pro
ve a central limit theorem for the joint distribution of the pair $(X_{\\e
ll}\,X_{\\ell'})$ for a wide range of $p$. Our proofs are based on the met
hod of moments and combinatorial arguments\, such as an algorithmic enumer
ation of collections of arithmetic progressions.\n\nThis is joint work wit
h Yacine Barhoumi-Andr\\'eani and Hong Liu (University of Warwick).\nSpeak
ers:\nChristoph Koch (Department of Statistics\, University of Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/50cd5e62-d126-4531-a276-f7ed5417f890/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:On the number of arithmetic progressions in sparse random
sets - Christoph Koch (Department of Statistics\, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mermin-Wagner Theorem for vertex-reinforced jump process - Roland
Bauerschmidt (Statslab\, University of Cambridge)
DTSTART;VALUE=DATE-TIME:20180604T120000
DTEND;VALUE=DATE-TIME:20180604T130000
UID:https://talks.ox.ac.uk/talks/id/2a0f9713-38ff-46ea-ab08-0de595401bbf/
DESCRIPTION:The vertex-reinforced jump process (VJRP) is a random walk tha
t prefers to jump to vertices visited in the past. Hyperbolic sigma models
are\nspin models where the spins take values in a hyperbolic space. I wil
l explain a relation between the VRJP and hyperbolic sigma models which\np
arallels that between the simple random walk and the Gaussian free field.
I will further show a Mermin-Wagner Theorem for hyperbolic sigma\nmodels w
hich implies that the VRJP is recurrent in two dimensions.\n\nThis is join
t work with Tyler Helmuth and Andrew Swan.\nSpeakers:\nRoland Bauerschmidt
(Statslab\, University of Cambridge)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/2a0f9713-38ff-46ea-ab08-0de595401bbf/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Mermin-Wagner Theorem for vertex-reinforced jump process
- Roland Bauerschmidt (Statslab\, University of Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limiting directions for random walks in affine Weyl groups - Arvin
d Ayyer (Indian Institute of Science\, Bangalore)
DTSTART;VALUE=DATE-TIME:20180521T120000
DTEND;VALUE=DATE-TIME:20180521T130000
UID:https://talks.ox.ac.uk/talks/id/16725332-6d01-4154-8d50-cce4c902cbf9/
DESCRIPTION:The multispecies totally asymmetric simple exclusion process (
MTASEP) is an interacting particle system defined on a finite one-dimensio
nal integer lattice with periodic boundary conditions. The exact stationar
y distribution of this Markov process was described by P. Ferrari and J. M
artin using multiclass M/M/1 queues. Recently\, T. Lam considered a random
walk on the alcoves of an affine Weyl group conditioned never to cross th
e same hyperplane twice. He proved that the limiting direction of this wal
k exists almost surely\, and conjectured a formula for it for \\tilde{A}_n
. I will describe joint work with S. Linusson\, where we solved this conje
cture by computing this limiting direction as certain correlations of the
MTASEP.\n\nTime permitting\, I will describe extensions of our work for th
e affine Weyl group \\tilde{C}_n. This involves the study of correlations
in a multispecies exclusion process with open boundaries (i.e.\, allowing
the entry and exit of particles). Here\, we have also computed this limiti
ng direction building on existing work of C. Arita\, in joint work with E.
Aas\, S. Linusson and S. Potka.\nSpeakers:\nArvind Ayyer (Indian Institut
e of Science\, Bangalore)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/16725332-6d01-4154-8d50-cce4c902cbf9/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Limiting directions for random walks in affine Weyl group
s - Arvind Ayyer (Indian Institute of Science\, Bangalore)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Four-dimensional loop-erased random walk and uniform spanning tree
- Wei Wu (Department of Statistics\, University of Warwick)
DTSTART;VALUE=DATE-TIME:20180514T120000
DTEND;VALUE=DATE-TIME:20180514T130000
UID:https://talks.ox.ac.uk/talks/id/b5d9bccd-240a-4cc9-bd84-c0624b627b7f/
DESCRIPTION:Critical lattice models are believed to converge to a free fie
ld in the scaling limit\, at or above their critical dimension. This has b
een established for Ising and \\Phi^4 models for d \\geq 4. We describe a
simple spin model from uniform spanning forests in Z^d whose critical dime
nsion is 4 and prove that the scaling limit is the bi-Laplacian Gaussian f
ield for d\\geq 4. At dimension 4\, there is a logarithmic correction for
the spin-spin correlation and the bi-Laplacian Gaussian field is a log cor
related field. The proof also improves the known mean field picture of LER
W in d=4: we show that the renormalized escape probability (and arm events
) of 4D LERW converge to some "continuum escaping probability". Based on j
oint works with Greg Lawler and Xin Sun. \n\nSpeakers:\nWei Wu (Department
of Statistics\, University of Warwick)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b5d9bccd-240a-4cc9-bd84-c0624b627b7f/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Four-dimensional loop-erased random walk and uniform span
ning tree - Wei Wu (Department of Statistics\, University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mallows permutations and stable marriage - Alexander Holroyd
DTSTART;VALUE=DATE-TIME:20180509T120000
DTEND;VALUE=DATE-TIME:20180509T130000
UID:https://talks.ox.ac.uk/talks/id/e9ff1f21-9776-4fcf-8e15-fa35f3c5f125/
DESCRIPTION:The Mallows measure on the symmetric group S_n assigns to each
permutation a probability proportional to a parameter q to the power of t
he inversion number. It was originally introduced in 1957 in the context o
f statistical ranking theory\, and has been used in many areas including s
tatistical physics\, learning theory\, mixing times\, and finite dependenc
e. Gale-Shapley stable marriage is a cornerstone of economic theory as wel
l a mathematical gem. Introduced in 1962\, it was the subject of the 2012
Nobel prize in economics\, awarded to Roth and Shapley. I'll explain how t
he two objects are related. In particular\, the former is an example of th
e latter. Among other things this gives a simple and elegant new descripti
on of the Mallows measure on the infinite line Z\, provided one does not g
et distracted by "wild matchings"!\nSpeakers:\nAlexander Holroyd
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e9ff1f21-9776-4fcf-8e15-fa35f3c5f125/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Mallows permutations and stable marriage - Alexander Holr
oyd
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max-Average Games with Random Payoffs - Rahul Santhanam (Departmen
t of Computer Science\, University of Oxford)
DTSTART;VALUE=DATE-TIME:20180430T120000
DTEND;VALUE=DATE-TIME:20180430T130000
UID:https://talks.ox.ac.uk/talks/id/2c8a4425-8850-49f9-b3d4-33d4d5e92550/
DESCRIPTION:Consider the following simple 2-person sequential game with i.
i.d. payoffs. The 2 players\, Max and Average\, each have exactly 2 option
s for each\nmove. Max plays optimally\, i.e.\, to maximize her payoff\, an
d Average plays randomly. How does the expected payoff for Max depend on t
he distribution on payoffs?\n\nI will describe the complexity-theoretic mo
tivation for this question\, and describe some preliminary results when th
e distribution on payoffs is Bernoulli.\n\nJoint work with Andy Drucker.\n
Speakers:\nRahul Santhanam (Department of Computer Science\, University of
Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/2c8a4425-8850-49f9-b3d4-33d4d5e92550/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Max-Average Games with Random Payoffs - Rahul Santhanam (
Department of Computer Science\, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
END:VCALENDAR